plane.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
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 * Copyright(C) 2021-2025                                                    *
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
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#ifndef VCL_SPACE_CORE_PLANE_H
#define VCL_SPACE_CORE_PLANE_H
 
#include "point.h"
 
#include <vclib/concepts/space/plane.h>
#include <vclib/exceptions/misc.h>
 
namespace vcl {
 
// TODO: Make Plane Serializable and add tests.
template<typename Scalar, bool NORM = true>
class Plane
{
    Point3<Scalar> mDir;
    Scalar         mOffset;
 
public:
    using ScalarType = Scalar;
    using PointType  = Point3<Scalar>;
 
    Plane() {}
 
    Plane(const Point3<Scalar>& direction, Scalar offset) :
            mDir(direction), mOffset(offset)
    {
        if constexpr (NORM) {
            Scalar n = mDir.norm();
            mDir /= n;
            mOffset /= n;
        }
    }
 
    Plane(const Point3<Scalar>& p0, const Point3<Scalar>& normal)
    {
        mDir = normal;
        if constexpr (NORM) {
            mDir.normalize();
        }
        mOffset = p0.dot(mDir);
    }
 
    Plane(
        const Point3<Scalar>& p0,
        const Point3<Scalar>& p1,
        const Point3<Scalar>& p2) :
            Plane<Scalar, NORM>(p0, (p2 - p0).cross(p1 - p0))
    {
    }
 
    template<typename S>
    auto cast() const
    {
        if constexpr (std::is_same<Scalar, S>::value) {
            return *this;
        }
        else {
            return Plane<S, NORM>(mDir.template cast<S>(), mOffset);
        }
    }
 
    const Point3<Scalar>& direction() const { return mDir; }
 
    Scalar offset() const { return mOffset; }
 
    Point3<Scalar> projectPoint(const Point3<Scalar>& p) const
    {
        Scalar k = p.dot(mDir) - mOffset;
        return p - mDir * k;
    }
 
    Point3<Scalar> mirrorPoint(const Point3<Scalar>& p) const
    {
        Point3<Scalar> mirr = projectPoint(p);
        mirr += mirr - p;
        return mirr;
    }
 
    bool operator==(const Plane& p) const
    {
        return mOffset == p.mOffset && mDir == p.mDir;
    }
 
    bool operator!=(const Plane& p) const { return !(*this == p); }
};
 
/* Specialization Aliases */
 
using Planef = Plane<float>;
using Planed = Plane<double>;
 
} // namespace vcl
 
#endif // VCL_SPACE_CORE_PLANE_H